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research-article

Analytical Structures of Takagi-Sugeno Fuzzy Two - Input Two - Output PI/PD Controllers with Multiple Fuzzy Sets

[+] Author and Article Information
Ritu Raj

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India 721302; Department of Electrical and Electronics Engineering, O P Jindal University, Raigarh, India 496109
riturajsam@gmail.com

Mohan Bosukonda Murali

Department of Electrical Engineering, Indian Institute of Technology, Kharagpur, India 721302
mohan@ee.iitkgp.ac.in

1Corresponding author.

ASME doi:10.1115/1.4042463 History: Received January 29, 2018; Revised December 23, 2018

Abstract

In this paper an attempt has been made to generalize the analytical structure of Takagi-Sugeno (TS) fuzzy Two-Input Two-Output (TITO) Proportional-Integral (PI) and Proportional-Derivative (PD) controllers using multiple input fuzzy sets. Two models of fuzzy TITO PI and PD controllers are proposed based on two distinct control strategies. The inputs are fuzzified by multiple fuzzy sets with trapezoidal/triangular membership functions. The generalized rule base consists of nine control rules imbibing the complete control strategy and is closer in spirit to TS rule base. Algebraic Product (AP) triangular norm, Bounded Sum (BS) triangular co-norm and Center of Gravity (CoG) defuzzifier are applied to derive the models. The models of the fuzzy TITO PI/PD controllers with multiple input fuzzy sets are (nonlinear) variable gain/structure controllers. Also, each output of the fuzzy controller is the sum of two nonlinear PI or PD controllers with variable gains. The gain variation and properties of the proposed controllers are studied. Two examples of nonlinear dynamic processes are considered to demonstrate the applicability of the proposed controllers.

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